Construction and Characteristic Analysis of Dynamic Stress Coupling Simulation Models for the Attitude-Adjustable Chassis of a Combine Harvester

Abstract

The combine harvester equipped with attitude-adjustment functionality significantly enhances its adaptability to complex terrain but often struggles to maintain the reliability of its mechanisms. Therefore, investigating the dynamic load characteristics of the attitude-adjustment mechanism becomes imperative. This article employed the DEM–FMBD (Discrete Element Method–Flexible Multibody Dynamics) bidirectional coupling simulation method to establish a multibody dynamic model of a tracked combine harvester. The study delved into the interaction mechanism and dynamic stress response characteristics between the tracked chassis and the complex terrain under various height adjustments, lateral adjustment angles, longitudinal adjustment angles, and different field-ridge crossing methods. Finally, the accuracy of the coupled simulation model was validated through a constructed stress detection system. The research findings revealed that the displacement and tilt angle deviation of the hydraulic cylinders utilized to execute the chassis adjustment actions in the constructed coupled simulation model was less than 5%, and the deviation between the simulation results and the actual maximum dynamic stress under multiple working conditions ranged from 7% to 15%. This verification confirmed the effectiveness of the DEM–FMBD coupled simulation method. Under different adjustment conditions, the maximum stress position was consistently distributed in the same area of the left-front and left-rear rotating arms. The primary and secondary effects of the various parts of the adjustment mechanism on the overall reliability of the chassis were as follows: left front > right front > left rear > right rear. By implementing the middle height with the adjustment strategy, the dynamic stress extreme value of the adjustment mechanism can be effectively reduced by 21.98%, thereby enhancing the structural stability of the chassis.

1. Introduction

The challenging terrain conditions in hilly areas significantly diminish the adaptability of combined harvesters during travel and operation, consequently heightening the risk of overturning. Adjusting the vehicle’s posture during operation can effectively mitigate this issue. Wheeled harvesters often achieve single-wheel ground clearance adjustment through hydraulic differential height mechanisms or by adding suspensions to the drive wheels [1,2]. Conversely, tracked harvesters enhance their chassis by integrating multilink adjustment mechanisms onto the existing fixed clearance chassis, thereby collectively adjusting with the frame and its upper load-bearing components [3].

Attitude-adjustable chassis are one of the key research areas in current agricultural machinery leveling systems. Wang et al. [4] designed a leveling mechanism and device to enhance the possibility of the track chassis under complex grounding conditions, using two electric cylinders and a steering gear to support and adjust the spatial angle of the vehicle body. Du et al. [5] proposed a leveling mechanism and validated it through field experiments. The results showed that leveling reduced harvest losses by 0.5%. Lü et al. [2] designed adaptive lateral and longitudinal leveling mechanisms and proposed corresponding control strategies. The experiments showed that the proposed leveling mechanism and control strategy could help the tracked chassis maintain level on inclined ground. Hu et al. [6] also proposed an adaptive leveling strategy, indicating that the proposed control system can control a horizontal error of ±0.4°.

Given the complexity of operating environments in hilly areas, designing reliable and durable attitude-adjustment mechanisms is particularly crucial. Any significant malfunction, such as fracture failure, occurring in the adjustment mechanism under external loads directly impacts the working efficiency and reliability of the harvester.

Therefore, achieving a balance between the reliability and stability of the chassis attitude-adjustment performance stands as a critical issue that demands immediate attention. Many scholars typically verify the structural strength of the chassis attitude-adjustment mechanism through a finite element analysis after completing its design. Sun et al. utilized Ansys to conduct static simulations on the frame and rotating arm components of a tracked combine harvester, optimizing the design of the vulnerable parts [3]. Similarly, Sun and Peng et al. determined the maximum stress and distribution position of the attitude-adjustment devices for tracked tractors, ensuring that they can withstand loads that are significantly below the yield strength while meeting the design requirements [7,8]. It is noteworthy that existing research on the reliability design of chassis adjustment mechanisms often concentrates on individual components, predominantly under static conditions. These studies typically impose artificially defined boundaries, constraint conditions, and external load inputs, disregarding the impact of walking mechanisms and soil on the entire attitude-adjustment system. This approach starkly contrasts with the actual operational conditions. Particularly concerning tracked walking chassis, a multifaceted interaction exists between the ground and the combine harvester’s tracks [9,10], with the polygonal effect generated by the track and the walking wheel system being a factor that cannot be overlooked.

The mature application of multibody dynamics (MBD) and discrete element method (DEM) simulation software (2021.2) offers effective technical solutions to the aforementioned challenges. The Recurdyn software (V9 R4), which is capable of modeling the dynamic behavior of rigid or elastic multibody systems, features integrated Multi Flexible Body Dynamics (MFBD) rigid–flexible coupling technology, which holds industry advantages in structural dynamic stress simulation. This software has been successfully employed in various engineering cases, including the stress analysis of coal mining machine rocker arm shells [11], the stability assessment of drone gimbals [12], and the compilation of stress spectra for flexible gears in gun steering machines [13]. Meanwhile, the discrete element method has emerged as the premier approach for simulating soil mechanical behavior. In recent years, it has found widespread use in examining soil loosening [14], soil deformation [15], and the interaction between tracks and soil [16]. Notably, the EDEM software (2021.2), among others, offers extensive soil databases, enriching materials for modeling complex terrains. However, due to the significant simplification and equivalent processing of models within a single software, accurately reflecting real-world operational scenarios becomes challenging. To address this, coupling technology has emerged, integrating DEM with MBD or MFBD. Zhao et al. [17] developed an MBD–DEM coupled simulation model for the threshing system of a harvester, optimizing the design of a corn biomimetic threshing component. Gan et al. conducted joint simulations of multibody dynamics and discrete elements for hydraulic excavators [18], illustrating the interactions between solid particles and excavators. Additionally, Zhang et al. demonstrated that bidirectional coupling between DEM and MFBD facilitates the accurate prediction of dynamic response characteristics and the fatigue life of drilling bits, offering valuable insights into fatigue strength design [19].

These studies collectively underscore the effectiveness of bidirectional coupling methods based on DEM and MBD/MFBD in accurately simulating the interaction between geometry and particles, thus offering a more realistic representation of actual operational conditions. Consequently, addressing the limitations of traditional finite element methods in studying the strength of chassis attitude-adjustment mechanisms, our paper focuses on a tracked combine harvester with an attitude-adjustment capability. It establishes a rigid–flexible coupling of the combine harvester’s chassis attitude-adjustment mechanism and a discrete element soil model of the complex terrain. Utilizing DEM-FMBD bidirectional coupling technology, this research investigates the interaction mechanism and dynamic stress response characteristics between the tracked chassis and the complex terrain under varying height adjustments, lateral and longitudinal angles, and different field-ridge crossing methods. Finally, the accuracy of the coupled simulation model is validated using the constructed stress detection system. This study not only introduces novel ideas and methodologies for the structural optimization design and reliability analysis of tracked attitude-adjustment chassis but also holds reference significance for related research on traditional tracked vehicles.

2. Materials and Methods

2.1. Composition of the Chassis Attitude-Adjustment System

The system of the 4LZ-4.0 tracked combine harvester equipped with a chassis attitude-adjustment system is illustrated in Figure 1. It is primarily comprised of an attitude-adjustment mechanism, a hydraulic valve group, a tilt sensor, an onboard controller, and a manual operation panel, enabling the overall lifting, lateral adjustment, and longitudinal adjustment actions. The system employs a tilt sensor to determine the inclination angle of the vehicle body, and a vehicle-mounted controller regulates the opening and closing of the solenoid valve, thereby driving the hydraulic cylinder to execute telescopic actions. The displacement sensor provides feedback on the cylinder’s displacement to the controller, forming a closed-loop system that ultimately accomplishes the attitude adjustment of the combine harvester.

In order to achieve the adjustment of the vehicle posture, the traditional chassis fixed beams connecting the chassis frame and the walking devices on both sides were eliminated, and the upper frame of the chassis was redesigned as a single fixed unit. The adjustment of the vehicle’s attitude was facilitated by the symmetrically distributed chassis attitude-adjustment mechanism. Each side of the adjustment mechanism comprised the front swivel arm, the connecting rod, the rear rotating arm, the rear swivel arm, the small swivel arm, the front hydraulic cylinder, and the rear hydraulic cylinder, as shown in Figure 2. Notably, the front and rear turning arms on both sides were rigidly connected via a spline shaft in the middle, ensuring no relative displacement between the connecting mechanisms. The remaining connecting mechanisms were hinged to enable relative rotation. Additionally, the spline shafts of the front and rear turning arms were individually hinged to the chassis frame, allowing the adjustment mechanisms on both sides to link the chassis frame to the walking device.

2.2. Principle Analysis of the Attitude Adjustment and Parameter Acquisition

The model of the attitude-adjustment mechanism was simplified to obtain the adjustment principle of the chassis, as depicted in Figure 3. Components 1–9 represent the left linkage mechanism, while 1*−9* represent the right linkage mechanism. Among these, 3 and 3* correspond to the front hydraulic cylinders, and 5 and 5* correspond to the rear hydraulic cylinders. Points A-O denote the various hinge points within the attitude-adjustment mechanism. When horizontally adjusting the chassis frame, ADEN forms a parallel four-bar mechanism, maintaining the length of rear hydraulic cylinder 5, while adjusting the length of front hydraulic cylinder 3. Under the influence of this parallel quadrilateral mechanism, arms NME and ABD rotate clockwise to elevate the frame. The simultaneous adjustment of the lengths of front hydraulic cylinders 3 and 3* enables the overall lifting of the chassis. For the longitudinal adjustment of the chassis frame, ADENO forms a parallel five-bar mechanism. Here, the length of front hydraulic cylinder 3 remains constant, while the length of rear hydraulic cylinder 5 changes. As point E descends, point D rises. The simultaneous movement of both rear hydraulic cylinders 5 and 5* results in the entire chassis tilting forward or backward.

The displacement of the hydraulic cylinders during the actual adjustment process was used as the driving condition for the simulation and analysis, which resulted in more reliable outcomes. To further clarify the attitude-adjustment parameters of the chassis, adjustment tests were conducted on the combine harvester under stationary conditions, focusing on lateral and longitudinal adjustment scenarios. The displacement of each hydraulic cylinder and the vehicle’s adjustment angle were recorded during the tests. A photo of the test site is shown in Figure 4, the red line in the figure is the horizontal line.

For clarification purposes, we used positive and negative signs to distinguish the direction of the attitude adjustment. Specifically, a negative sign was used to denote left and backward tilt angles. The measured data for the lateral adjustment and the overall lifting height are presented in Figure 5. Observing Figure 5, it is evident that the displacement of the two rear cylinders remains constant. Within the initial 15 s, the chassis underwent a lateral adjustment, with the displacement of the two front cylinders changing by 65 mm. During this period, the maximum ground clearance of the frame, as measured with a ruler, was approximately 100 mm. Between 15 and 28 s, when only the left-front cylinder extends by 65 mm, the maximum tilt angle of the chassis to the right is 5.15°. Subsequently, from 30 to 42 s, when only the right-front cylinder extends by 65 mm, the maximum left tilt angle of the chassis is 5.55°. Consequently, the lateral adjustment range of the attitude adjustment chassis spans from −5.18° to 5.55°. It is noteworthy that the discrepancies in the left and right limit adjustment angles may arise from actual assembly errors.

The longitudinal adjustment data are depicted in Figure 6. Because of the longitudinal horizontal position of the chassis, the two rear hydraulic cylinders have already extended by 30 mm. If we define this position as zero, the corresponding retraction of 30 mm is defined as −30 mm. Within the initial 22 s of the chassis longitudinal adjustment, with the extension of the two front hydraulic cylinders at 0 mm and the chassis at its lowest position, the displacement of the two rear cylinders synchronously changed by −30 mm to 45 mm. Consequently, the longitudinal change in the angle range of the chassis spans from −3.13° to 5.15°. From 25 to 42 s, as the two front cylinders extend by 65 mm and the chassis reaches its highest position, with the two rear cylinders synchronously changing by −30 to 45 mm, the longitudinal angle range of the chassis is from −4.06° to 4.55°. Thus, the adjustable longitudinal range of the chassis for this attitude adjustment is from −4.06° to 5.15°.

2.3. Construction of the DEM–FMBD Rigid–Flexible Coupling Model

2.3.1. FMBD Model Construction for the Combine Harvester

Using the Solidworks software (Solidworks 2020, Dassault Systèmes, Waltham, MA, USA), the construction of a tracked combine harvester model with the attitude-adjustable chassis was completed based on the existing physical prototype. The 3D model was then imported into the LM track module of Recurdyn (Recurdyn2020, FunctionBay, Inc., Seoul, Republic of Korea). Rubber tracks were added to the model based on the assembly and constraint relationships between the walking wheel systems, followed by the completion of the overall constraint and contact settings. The weight of each component of the harvester above the frame was added according to the actual weight specifications, resulting in the establishment of the MBD multibody dynamics model depicted in Figure 7. Within the attitude-adjustment mechanism, the front and rear swivel arms serve as the primary adjustment components for adjusting the chassis posture of the tracked combine harvester. They must not only withstand gravity from the entire machine and the driving force from the cylinders, but also endure the impact loads from the frame and the walking mechanism. Consequently, they represent the weak links in the chassis attitude-adjustment mechanism.

During operation, the load borne by the rotating arms induces elastic deformation. Compared with multi-rigid-body systems, rigid–flexible coupling systems can fully account for the influence of flexible deformation and rigid body motion, thereby enhancing the reliability of the simulation results. Considering the nonlinear mechanical behaviors of tracks and soil [20], the FFLEX (Full Flex, used in the modeling and simulation of flexible bodies) method should be employed to construct a rigid–flexible coupled multibody dynamic model based on a multi-rigid-body model [13,14]. Using the grid partitioning software Hypermesh (Hypermesh2020, Altair Engineering, Troy, MI, USA), the front and rear rotating arms were meshed. We compared the maximum stress output results across different levels of mesh refinement within the 5–20 mm mesh size range. It was observed that when the mesh size was reduced to below 10 mm, the variation in the simulation results stabilized within 3%. This indicates that the simulation results were no longer dependent on the mesh size. To balance accuracy and computational efficiency, the final mesh size was determined to be 10 mm. After conducting the mesh independence verification, parameters such as the number of grid nodes, the number of grid elements, and the material properties were obtained, as shown in

Table 1. Material and grid properties.

Project	Parameter	Project	Parameter
Material	40Cr	Grid size, mm	10
Young’s modulus, GPa	206	Node number of the left/right front rotating arm	4788
Poisson’s ratio	0.29	Element number of the left/right front rotating arm	16,314
Density, kg/m3	7850	Node number of the left/right rear rotating arm	3863
Yield strength, MPa	500	Element number of the left/right rear rotating arm	12,327

. The processed rotary arm model was then imported into the rigid-body model, replacing the original part to complete the flexibility operation, and the contact between the flexible body and the rigid frame was re-established. To ensure an effective force transfer between the flexible and rigid bodies, the FDR unit between the hole axis was established, ultimately completing the FMBD model of the tracked chassis attitude-adjustment mechanism, as depicted in Figure 8.

After constructing the rigid–flexible coupling model, it is crucial to verify whether the model can replicate the same adjustment actions and parameters as the actual prototype. To achieve this, the measured displacement data on the hydraulic cylinders in Section 2.1 were imported into the model as the STEP function, serving as the driving data for the hydraulic cylinders’ movement. The snapshot of the attitude-adjustment mechanism during the adjustment process is presented in Figure 9, with the adjustment actions within each working cycle aligned with the actual working conditions. We have calculated the range of the cylinder expansion and contraction, the overall lifting height, and the vehicle inclination angle under different adjustment conditions. The cylinder displacement matched the actual prototype variation, resulting in an overall lifting height range of 0–102.33 mm, a maximum limit lateral adjustment angle range of −5.46° to 5.84°, and a maximum limit longitudinal adjustment angle range of −4.28° to 5.46°. From these data, it is evident that the FMBD model effectively executes the lateral and longitudinal adjustment actions of the chassis attitude, while considering the force deformation of the rotary arms. The error between the adjustment parameters of the rigid–flexible coupling model and the actual physical prototype adjustment parameters was less than 5%, meeting the requirements of practical engineering applications.

2.3.2. DEM Model Construction for Complex Terrains

Accurate terrain simulation is pivotal for comprehending the walking characteristics of tracked combine harvesters, aiding in the analysis of how alterations in the harvester and terrain impact its dynamic load characteristics. A soil model construction commenced with defining parameters, such as the bulk density and the angle of repose, followed by sourcing particle reference models from the GEMM database of EDEM (EDEM2021.2, DEM Solutions Ltd., Edinburgh, UK). Simultaneously, to manage the particle count and enhance the computational efficiency, a basic particle diameter of 5 mm was chosen, with randomly generated particles ranging from 0.5 to 1.5 times the basic particle size. Parameters like the recovery coefficient, the static friction coefficient, and the rolling friction coefficient of particles were selected and adjusted accordingly. To ensure that the mechanical properties of soil particles on the field road surface align with reality, the Hertz–Mindlin contact model with adhesion was utilized. Building upon prior research by our research group and Fu et al.’s reference [16,21,22], the parameter calibration for the soil model was completed.

Table 2. DEM parameters for simulation.

Project	Parameter	Project	Parameter
Poisson’s ratio of soil	0.3	Track–soil recovery coefficient	0.5
Density of soil, kg/m3	2000	Track–soil friction coefficient	0.45
Shear modulus of soil, MPa	6 × 106	Track–soil rolling friction coefficient	0.01
Soil–soil recovery coefficient	0.55	Physical radius, mm	5
Soil–soil static friction coefficient	0.2	Contact radius, mm	6
Soil–soil rolling friction coefficient	0.01	Normal stiffness, N/m	5 × 108
Density of the track, kg/m3	7680	Shear stiffness, N/m	5 × 107
Poisson’s ratio of track	0.3	Shear strength, MPa	3.2 × 106
Shear modulus of track, MPa	7.2 × 1010	Tensile strength, MPa	2.6 × 106

provides an overview of the DEM parameters employed in the simulation.

To model the soil terrain, dynamic particle factories were integrated into EDEM to facilitate the complete particle filling of the entire road surface. Given the substantial number of particles in the soil model, the DEM soil simulation model was distributed across multiple GPU processors, and a dynamic computing domain was implemented. This domain resolved only the particles within the computing domain at each time step, significantly reducing the computational time required for the particle contact detection and GPU utilization. We conducted a comparison of solving speeds with traditional CPU devices, revealing a 5–8 times improvement in the solving speed when employing the former. The final established soil particle bed model is depicted in Figure 10.

2.3.3. Track–Soil Bidirectional Coupling Model

During the operation of a tracked combine harvester, the tracks remain in constant contact with the soil particles, facilitating the exchange of information between Recurdyn and EDEM. The tracked combine harvester model established in Recurdyn and the soil model established in EDEM share the same global coordinate system. Only the two tracks on both sides were exported in a wall file format and imported into the EDEM soil model, where the corresponding spatial position relationship was defined to enable force transmission. The two software programs were bidirectionally coupled via the external SPI interface to achieve real-time data exchange between the soil particles and geometric models. The principle of bidirectional coupling between EDEM and Recurdyn is illustrated in Figure 11.

Based on the measured displacement data on the hydraulic cylinders, STEP functions for each oil cylinder in Recurdyn were set as Step (TIME, T₁, x₁, T₂, x₂). This function drives the oil cylinder to achieve displacement changes from x₁ to x₂ within the time interval T₁ to T₂, enabling overall lifting, lateral adjustment, and longitudinal adjustment of the chassis. Horizontal ground, horizontal slope, vertical slope, and field ridge terrains were established in Solidworks, imported into EDEM, and modelled using soil particle beds to replicate the complex terrain. Coupled simulation models under various adjustment conditions were constructed and solved through bidirectional coupling interfaces. During the calculation process, the EDEM software timestep was set to 20% of the Rayleigh timestep, with data saved every 0.1 s. In the Recurdyn software, data were saved every 0.01 s. The final established coupled simulation model is depicted in Figure 12.

2.4. Construction of the Dynamic Stress Testing System

By integrating resistance strain gauges with specialized dynamic stress detection systems, we can effectively monitor and record the dynamic stress of the mechanism. This stress detection method has a mature technical solution in the engineering field [23,24]. In this study, we evaluated the coupled simulation model by monitoring the dynamic stress data on key measurement points. The strain gauges utilized were standard 45° triaxial strain gauges capable of measuring strain in three directions, as illustrated in Figure 13. The maximum and minimum principal stresses can be calculated using the strains in three directions. The equivalent stress can be obtained using Formulas (1)–(3) [25,26].

$${\delta }_1={\displaystyle \frac{E}{2}}\left[{\displaystyle \frac{{\epsilon }_a+{\epsilon }_c}{1-\mu }}+{\displaystyle \frac{\sqrt{2}}{1+\mu }}\sqrt{{\left({\epsilon }_a-{\epsilon }_b\right)}^2+{\left({\epsilon }_b-{\epsilon }_c\right)}^2}\right]$$

(1)

$${\delta }_2={\displaystyle \frac{E}{2}}\left[{\displaystyle \frac{{\epsilon }_a+{\epsilon }_c}{1-\mu }}-{\displaystyle \frac{\sqrt{2}}{1+\mu }}\sqrt{{\left({\epsilon }_a-{\epsilon }_b\right)}^2+{\left({\epsilon }_b-{\epsilon }_c\right)}^2}\right]$$

(2)

The equivalent stress was calculated using the fourth strength theory:

$${\delta }_S=\sqrt{0.5\left[{\left({\delta }_1-{\delta }_2\right)}^2+{{\delta }_1}^2+{{\delta }_2}^2\right]}$$

(3)

where a, b, and c represent the three strain gauges, respectively; E is the elastic modulus of the material, MPa; μ is the Poisson’s ratio of the material; ε_a, ε_b, and ε_c represent the strain for strain gauges a, b, and c, respectively; δ₁ and δ₂ represent the maximum and minimum principal stresses, MPa; δ_S is the equivalent stress, MPa.

According to the simulation results, strain gauges were placed on the surface of the structure in the areas of maximum stress distribution using the correct pasting method. They were then connected to the DH5902N dynamic stress measurement system. The sampling frequency was set to 500 Hz, and the maximum stress values of the key measuring points under different working conditions were measured and recorded. The configuration of the dynamic stress detection system is illustrated in Figure 14. Given the continuous adjustment process of the attitude-adjustment mechanism during the experiment, which involved a significant amount of data and manual calculation, the Ncode software (2023) was utilized for processing the experimental data. The Ncode software was commonly employed for stress analysis data processing. It utilizes the Strain Rosette module to calculate the maximum principal stress and exports the data through the Series Output module.

2.5. Evaluation Methods

2.5.1. Average Stress of Attitude-Adjustable Chassis

The maximum stress observed in the simulation of rigid–flexible coupling did not typically occur at a specific location but often fluctuated within a certain region. Therefore, relying solely on the maximum stress of a single node made it challenging to analyze the true stress state of the regulating mechanism. Instead, it can only serve as a reference for the changes in structural stress trends. To accurately depict the dynamic characteristics of dynamic loads on the loaded driving of the adjustment mechanism, the maximum stress of multiple nodes was calculated, and the average stress was determined. The calculation formula was as follows:

$${\delta }_F={\displaystyle \frac{{\displaystyle \sum _{i=1}^n{\delta }_{Max}}}{n}}$$

(4)

In the formula: δ_F is the average stress; δ_Max is the dynamic stress obtained by a single node during the dynamic adjustment process, MPa; n refers to the number of nodes where the adjustment mechanism produces the maximum stress during driving. The smaller the average stress, the less load the mechanism is subjected to, and the more stable the structure is.

2.5.2. Overall Reliability of Attitude-Adjustable Chassis

The average stress can characterize the dynamic characteristics of a single component structure. However, the dynamic stress of a single mechanism may not fully represent the reliability of the entire mechanism. The literature suggested that a Gaussian function can be employed to depict the mapping relationship between the stress of a single component and the reliability of the structure [27]. The constructed stress reliability membership function is shown in Formula (5).

$$R_S={\mu }_S\left(x\right)=\left\{\begin{array}{c}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}1\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em},0<x\le a\hspace{1em}\\ \exp \left[-{\displaystyle \frac{1}{2}}{\left({\displaystyle \frac{2\left(x-a\right)}{\lambda }}\right)}^2\right]\hspace{1em},0<x\le b\end{array}\right.$$

(5)

where, x represents the maximum dynamic stress of the stable stage structure; a denotes the allowable stress of the material, where 250 MPa is adopted when the safety factor is 2; and b stands for the yield limit of the material, taken as 500 MPa. λ is the scale parameter, which was taken as 80 in the paper [28]. The constructed membership function curve is depicted in Figure 15.

Transforming the stress information obtained from the dynamic simulation into corresponding reliability through membership functions is crucial. In the event of damage to a component in the adjustment mechanism, the entire chassis may not function properly. Therefore, the overall reliability coefficient R(x) of the chassis can be calculated according to Formula (6) [27]:

$$R\left(x\right)=R_1\left(x\right)\cdot R_2\left(x\right)\cdot R_3\left(x\right)\cdots \cdot R_n\left(x\right)={\displaystyle {\prod }_{i=1}^n}{R}_i\left(x\right)$$

(6)

where, x is the stress of any component in the adjustment mechanism, MPa; n is the number of components of the chassis attitude-adjustment mechanism; and R_i(x) represents the reliability of the component with the identifier i. The closer the reliability coefficient is to 1, the more reliable the overall chassis structure.

2.5.3. Equivalent Impact Stress of Attitude-Adjustable Chassis

Crossing the field ridge is one of the representative working conditions that a combine harvester needs to experience during field transfer. When a harvester crosses a field ridge, it often encounters an instantaneous impact load from the outside. To characterize the impact stress generated by the impact load during the continuous process of the harvester, the maximum stress at the moment of continuous impact was measured. The impact stress during the crossing process was calculated using a weighted method, denoted as the equivalent impact stress [29,30]. It can be calculated according to the following formula:

$${\delta }_E={\eta }_1{\delta }_1+{\eta }_2{\delta }_2+{\eta }_3{\delta }_3\cdot \cdot \cdot +{\eta }_m{\delta }_m$$

(7)

where, δ_E is the equivalent impact stress of the adjustment mechanism, MPa; m is the number of consecutive impact moments; δ_m is the impact stress at every impact moment, MPa; and η_m represents the stress weight for every impact moment, determined based on the proportion of the stress extremum to the average stress. In this study, the weights for three instantaneous impact stresses were respectively set to 0.2, 0.5, and 0.3 [31].

3. Results

3.1. Influence of Height Adjustment on the Dynamic Stress

The stress cloud diagram of the attitude-adjustment mechanism under different adjustment heights is depicted in Figure 16. For clarity, the particles and upper frame components are hidden. According to Figure 16a–e, it was observed that the maximum stress distribution of the front rotating arm occurred near the articulated area between the curved plate and the connecting rod of the front rotating arm, specifically in regions A and B. Similarly, the maximum stress distribution of the rear rotating arm was concentrated near the turning point between the rotating arm and the shaft, specifically in regions C and D, as shown in Figure 16e.

The maximum dynamic stress curves of the four rotary arm mechanisms under the overall lifting condition were extracted, taking the stress curve under the lowest ground clearance condition as an example, as shown in Figure 17. In the first 3 s, the harvester accelerated from stationary to 1.0 m/s. During this period, due to the inertia impact, the stress of each adjustment mechanism increased instantly, followed by a rapid drop back to the normal level. From 4 s to 10 s, the chassis maintained the lowest ground clearance and moved forward at a constant speed in a horizontal attitude. The peak stress of each mechanism fluctuated, which was attributed to the polygonal effect of the track. The overall trend of the dynamic stress curves of the four rotating arms was similar, but significant differences existed in the peak values. The average value of the maximum stress data of each mechanism when the harvester moved forward at a constant speed under different adjustment heights was calculated, as shown in Figure 18. Based on the stress cloud map, it was observed that the maximum stress areas of the four rotating arms were symmetrically distributed on both sides, but the stress extremes differed. The order of magnitude was left-front rotating arm (301.68–199.18 MPa) > right-front rotating arm (295.01–190.88 MPa) > left-rear rotating arm (169.29–122.67 MPa) > right-rear rotating arm (137.49–74.14 MPa), all of which were below the yield strength of the materials used. It was evident that as the chassis height increased, the stress extremes of the left- and right-front rotating arms gradually decreased, while those of the left- and right-rear rotating arms gradually increased. This aligns with the actual force distribution: during the rotation of the front rotating arm, its relative force arm to the hinge point on the walking mechanism gradually increased, while the force arm of the rear rotating arm gradually decreased. Consequently, the load on the hinge point of the front rotating arm decreased, and that of the rear rotating arm increased accordingly.

From the perspective of the reliability coefficient of the mechanism, the reliability coefficient of the two rear rotating arms remained consistently at 1, while the reliability of the left-front rotating arm was the lowest. However, it showed an increasing trend with the rise of the chassis height, and was positively correlated with the overall reliability of the chassis. After the adjustment height reached 50 mm, the structural reliability of the entire chassis approached 1. This indicated that although lowering the chassis to its lowest position during operation can lower the center of mass height and enhance the stability of the harvester, it can also reduce the overall reliability of the chassis to 0.82, increasing the risk of adjustment mechanism failure. As shown in Figure 19. On the other hand, appropriately raising the chassis height helped to ensure the structural stability of the chassis to a certain extent.

3.2. Influence of the Longitudinal Adjustment Angle on the Dynamic Stress

The stress cloud diagram of the adjustment mechanism under different longitudinal adjustment angles is depicted in Figure 20. Figure 20a–e illustrated the stress variation of the adjustment mechanism from the extreme backward tilt to the extreme forward tilt adjustment angles. According to the stress cloud diagram, under the five longitudinal adjustment attitudes, the maximum stress distribution position of the front rotating arm of the mechanism occurred near the arc plate of the front rotating arm and the hinge point of the connecting rod. Similarly, the maximum stress of the rear rotating arm was concentrated near the turning point of the rotating arm, which aligned with the maximum stress distribution area specified in Section 3.1.

The maximum dynamic stress curves of the four rotating arms under longitudinal adjustment conditions were extracted, using the stress curve with a maximum forward tilt of 5° as a representative example, as illustrated in Figure 21. During the initial 3 s, the harvester underwent acceleration from a stationary state to 0.8 m/s. At this juncture, the stress in each rotating arm experienced an instantaneous increase due to the impact of inertia, followed by a rapid decline in the peak stress. Subsequently, from 4 s to 8 s, the harvester commenced reciprocal adjustments, while between 8 s and 12 s, it completed an uphill movement while maintaining a horizontal attitude. Following the adjustment of the chassis to a horizontal state at various angles, the maximum stress data of each mechanism were analyzed to calculate the average value, as depicted in Figure 22. The extreme stress values for each mechanism ranked in the following order: left-front rotating arm (320.37–283.83 MPa) > right-front rotating arm (303.73–283.83 MPa) > left-rear rotating arm (123.92–112.27 MPa) > right-rear rotating arm (89.80–73.18 MPa). Notably, all the recorded stress values remained below the yield strength of the material.

It is evident that throughout the longitudinal adjustment process, spanning from the maximum forward tilt to the maximum backward tilt, the stress amplitude of the front rotating arms exhibited a pattern of initial decrease followed by stabilization, whereas the stress amplitude of the rear rotating arm remained relatively constant. This observation aligned well with the actual dynamic force. The longitudinal adjustment altered the distribution position of the harvester’s center of gravity along the longitudinal axis. During forward tilting, the center of gravity shifted forward, whereas during backward tilting, it shifted rearward. However, this variation appeared to be limited and exerted minimal influence on the stress fluctuations of the adjustment mechanism. Despite the rear rotating arms’ ability to share a portion of the overall load of the harvester, the majority of the load was still borne by the front rotating arms. Consequently, in the longitudinal adjustment mode, the force distribution of the front rotating arms held greater significance for ensuring the structural stability of the entire chassis.

This conclusion was further substantiated by the reliability coefficient analysis. Throughout the range from the maximum backward tilt to the maximum forward tilt, the reliability of both rear rotating arms consistently registered at 1. Meanwhile, the reliability coefficient of the left-front rotating arm consistently exhibited the lowest values. Notably, the overall reliability coefficient of the chassis demonstrated a positive correlation with the reliability of the two front rotating arms, reaching its nadir value of 0.75 during the extreme forward tilt state of 5°, as shown in Figure 23.

3.3. Influence of the Lateral Adjustment Angle on Dynamic Stress

In essence, the lateral adjustment mode represents a specialized case of the lifting adjustment mode. Through the manipulation of the differential extension and contraction of the two front hydraulic cylinders, the chassis can be inclined to the left or right, thereby enabling it to maintain a horizontal orientation on lateral slopes. Figure 24 presents the stress cloud diagram of the chassis mechanism across varying lateral adjustment angles. Specifically, Figure 24a–e depict the stress variations of the lifting mechanism ranging from the extreme left tilt to the extreme right tilt adjustment angles. Even across five lateral adjustment attitudes, the maximum stress positions of the front and rear rotating arms of the lifting mechanism persisted within the same region observed in the initial two adjustment modes.

The maximum dynamic stress curves of the four rotating arms were extracted under five working conditions, with reference to the stress curve when the left side was lifted by 5°, as illustrated in Figure 25. During the initial 3 s, the harvester accelerated from a stationary position to 1.0 m/s. The impact of inertia led to an instantaneous increase in stress within each adjustment mechanism, followed by a rapid decline in peak stress. Subsequently, between 4 s and 8 s, the harvester initiated lateral adjustment actions while moving forward. From 8 s to 12 s, the harvester completed a uniform lateral movement in a horizontal attitude. During the lateral climbing stage, it was observed that the stress on the two front rotating arms remained relatively stable, whereas the stress on the two rear rotating arms exhibited a trend of an initial increase followed by stabilization. The stress data were selected from the stable stages of each mechanism to calculate the average stress, as depicted in Figure 26. In the stable stage, the average stress of each rotating arm was as follows: left-front rotating arm (300.23–232.13 MPa) > right-front rotating arm (263.93–211.12 MPa) > left-rear rotating arm (167.33–102.95 MPa) > right-rear rotating arm (125.91–66.55 MPa). Notably, all the recorded stress values remained below the yield strength of the material.

Compared with non-adjustable working conditions, when the chassis was tilted left or right on a slope, there was a decrease in stress on the front rotating arm and an increase in stress on the rear rotating arm. This phenomenon arose due to the lateral shift in the harvester’s center of gravity, resulting in a redistribution of the load on each adjustment mechanism. The increased load borne by the rear rotating arm partially alleviates the pressure on the front rotating arm. The overall reliability coefficients of each rotating arm and the lifting chassis were calculated, as depicted in Figure 27. It can be observed that the chassis reliability coefficient was the lowest among the five operating conditions without adjustment, while under adjusted conditions, the overall chassis reliability coefficient consistently exceeded 0.95. This finding suggested that adjusting the lateral attitude of the chassis on a lateral slope not only enhanced the driving stability of the chassis but also significantly improved the reliability of the chassis structure. This conclusion aligns with the findings of Sun et al. [32]. Hence, when operating the harvester on a lateral slope, timely adjustment of the chassis lateral posture should be considered by the operator.

3.4. Influence of the Field-Ridge Mode on Dynamic Stress

Based on the influence of the adjustment parameters outlined in Section 3.1, Section 3.2 and Section 3.3 on the stress of the adjustment mechanism, it is advisable for the harvester to elevate the chassis height appropriately and perform longitudinal attitude adjustments when crossing ridges in fields. This approach helps to mitigate the impact of external loads on the adjustment mechanism while ensuring chassis maneuverability. Therefore, leveraging both actual driving experience and the analytical findings from previous sections, this section delves into four field-ridge adjustment modes: the lowest position (Mode 1), the lowest position with longitudinal adjustment combined (Mode 2), the middle position (Mode 3), and the middle position with longitudinal adjustment combined (Mode 4). The dynamic stress of the adjustment mechanism under each mode was analyzed. For safety considerations, this study excluded the field-ridge condition at a maximum height.

Figure 28 presents a snapshot of the scenario where the chassis remains in the middle position and undergoes forward and backward tilt motions during the crossing process. Throughout the entire process of traversing the field ridge, it was crucial to focus on the instantaneous impact load at three key moments: at 10.2 s, when the harvester’s driving wheel partially reached the field ridge, with the center of gravity not yet entirely crossing the ridge; at 12.4 s, when the harvester’s driving wheel made contact with the ground, signifying the complete crossing of the field ridge by the center of gravity; and at 14.1 s, when the guide wheel section descended from the field ridge to the ground, causing the track to be completely disengaged from the field ridge. The analysis of the stress cloud map results revealed that at the above three moments, the maximum stress positions consistently occurred in the left-front and left-rear rotating arms. This observation remained consistent with the conclusions drawn from conventional working conditions.

The dynamic stress curves of the left-front and left-rear rotating arms were statistically analyzed under four modes, along with their instantaneous stress extremes at the specified time points. The results are presented in Figure 29. From Figure 29, it is evident that Mode 4 offered the optimal crossing scheme, as indicated by the lower stress extreme points of the left-front rotating arm compared with the other three modes. Furthermore, the equivalent impact stresses of each mechanism under the three instantaneous impact loads were calculated throughout the crossing process. In comparison with the other modes, Mode 4 demonstrated significant improvements in the equivalent impact stresses of the left-front rotating arm, with enhancements of 19.06%, 21.98%, and 8.22%, respectively. Similarly, the equivalent impact stresses of the left-rear rotating arm increased by 8.82%, 14.36%, and 6.58%, respectively. The observed increase in the equivalent stress of the rear rotating arm can be attributed to the longitudinal adjustment action of the chassis. However, this adjustment aimed to alleviate the impact load on the front rotating arm and maintained the stress balance across the entire mechanism.

Figure 30 illustrates the trend in changes in the overall reliability of each rotating arm mechanism and the chassis across four different field-ridge modes. Both the front rotating arms and the chassis attained maximum reliability in Mode 4, while the overall reliability of the chassis remained below 0.6 in the other three modes. In summary, for tracked combine harvesters equipped with attitude-adjustment functions, the preferred strategy for drivers during field crossings involved setting the chassis height to the middle position and promptly adjusting the longitudinal posture of the chassis as needed throughout the crossing period. This approach ensured the overall passability of the machine and enhanced the stability of the adjustment mechanism.

3.5. Verification Test of Dynamic Stress

Based on the simulation test results, the maximum stress distribution position of the lifting mechanism was identified. To further validate the accuracy of the simulation model, a stress testing system was assembled using the DH5902N stress analyzer. Three-axis strain gauges were affixed to the maximum stress positions of the left-front and left-rear rotating arms, following the steps outlined in the simulation results. Subsequently, dynamic stress tests were conducted on the existing lifting chassis under various working conditions. The testing experiment took place at the Shi Yezhou rice experimental field in Zhenjiang City, Jiangsu Province. The terrain scene was artificially constructed to mimic the simulation scenario. The experimental site is depicted in Figure 31. The maximum stress under various working conditions was calculated, including the maximum lifting height, the maximum front and rear tilt, the maximum left and right tilt, the middle height with no adjustment, and the middle height with adjustment. For each working condition, we conducted three tests and calculated the average value of the maximum stress. The stress test results are summarized in

Table 3. Test results of the dynamic stress extreme values.

Adjusting Working Conditions	First Point			Second Point
	Simulation Value/MPa	Measured Value/MPa	Testing Error/%	Simulation Value/MPa	Measured Value/MPa	Testing Error/%
Lowest position	301.68	286.29	5.11	122.67	116.78	4.83
Highest position	199.18	187.03	6.15	169.26	159.78	5.65
Maximum left tilt	232.13	220.98	4.86	102.95	99.03	3.88
Maximum right tilt	264.12	247.74	6.27	129.31	122.32	5.44
Maximum front tilt	320.23	303.25	5.39	123.92	118.59	4.36
Maximum rear tilt	283.83	269.92	4.98	112.27	105.75	5.82
Middle height with no adjustment	355.89	315.31	11.44	326.62	284.81	12.83
Middle height with adjustment	325.96	282.93	13.20	304.49	260.03	14.60

.

According to Table 3, the test deviation for all the working conditions, except for the field-ridge condition, was within 7%. This suggested that the actual test results aligned closely with the simulation results, validating the use of the established coupled simulation model in studying the dynamic stress characteristics of attitude-adjustment mechanisms. Some significant deviation was observed in the field-ridge working condition, reaching a maximum of 14.6%. This deviation arose from variations between the actual driver operation and simulation conditions. Nonetheless, we observed a significant reduction in the stress extreme value of the mechanism after implementing the front and rear adjustment actions, consistent with the simulation results. This preliminary verification underscores the effectiveness of the field-ridge adjustment strategy.

4. Discussion

This study presented a tracked combine harvester rigid–flexible coupling simulation model that accurately captured the dynamic stress characteristics of the attitude-adjustment mechanism. It preliminarily verified that the DEM–MFBD bidirectional coupling technology could accurately simulate the interaction between the tracked combine harvester and the soil particles, providing a more realistic reflection of the actual loading conditions of the attitude-adjustment mechanism [11,12]. The simulation results indicated a significant relationship between the adjustment parameters and the dynamic stress of the attitude-adjustment mechanism, which aligned with the findings of Sun et al. [7]. The DEM–FMBD coupling simulation model comprehensively considered the impact of the track and the complex terrain on the attitude-adjustment mechanism, with dynamic stress deviations not exceeding 7%, demonstrating a good consistency with real conditions. This was a capability that static finite element analysis methods, such as those used by Hu et al. [3,5], could not achieve for individual parts and stationary conditions.

The results of this study are of significant importance for practical production processes. For the combine harvester, which operates in highly variable and complex working environments, many conditions are difficult to predict, especially in scenarios like crossing ridges and pits that are challenging and potentially hazardous to test in reality. The simulation remains a crucial solution to consider, and such approaches have been successfully applied in simulations of dangerous scenarios, like field overturning in tractors [33,34].

It is important to note that in crossing-ridge conditions, the dynamic stress test results showed deviations exceeding 10% compared with the simulation results. This discrepancy might have been due to differences between the ridge particle model and the general soil models, highlighting a limitation of the model established in this study. Therefore, it is necessary to develop a more accurate ridge soil model to improve the simulation precision in crossing-ridge conditions. In the future, we will also consider the effects of different soil moisture levels, grain tank weights, and other factors on the dynamic stress of the mechanism, construct dynamic stress spectra for the chassis attitude-adjustment mechanism, and conduct related fatigue life testing. These efforts are currently underway.

5. Conclusions

A simulation model based on DEM and FMBD bidirectional coupling technology was developed using measured data on the existing chassis of tracked combine harvesters. The dynamic stress of the adjustment mechanism under various conditions was statistically analyzed, and the model was validated through a constructed stress detection system. The research findings were as follows:

(1)

The bidirectional coupling simulation model of DEM and FMBD enables the completion of overall lifting, lateral adjustment, longitudinal adjustment, and field-ridge adjustment actions on complex terrain. The displacement and tilt angle deviation of the oil cylinder were all within 5%, maintaining a good consistency with the physical prototype.

(2)

Under different adjustment conditions, the maximum stress position was consistently distributed in the same area of the left-front rotating arm and the left-rear rotating arm. Each mechanism’s maximum dynamic stress satisfied the yield strength of the material.

(3)

During the overall lifting, the maximum dynamic stress of the adjustment mechanism decreased as the chassis height increased, leading to improved overall reliability. In longitudinal adjustment conditions, the maximum stress of the left-front rotating arm increased with the inclination angle, and the overall reliability of the chassis reached its lowest level in the longitudinal forward tilt attitude. Lateral adjustment, by adjusting the left and right tilts, can reduce the extreme dynamic stress of the adjustment mechanism, thereby enhancing the overall reliability of the chassis.

(4)

Adopting the middle height with the adjustment strategy resulted in a significant reduction of 19.06%, 21.98%, and 8.22% in the dynamic stress extreme value of the adjustment mechanism compared with other modes, thereby improving the structural stability of the chassis.

(5)

The deviation between the simulation results of conventional regulation conditions and the actual maximum dynamic stress was within 7%, while the maximum dynamic stress deviation under field-ridge conditions was within 15%, further validating the accuracy of the DEM–FMBD coupled simulation model.